{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "129937c8",
   "metadata": {},
   "source": [
    "# Modeling distributions\n",
    "\n",
    "The distributions we have used so far are called **empirical\n",
    "distributions** because they are based on empirical observations, which\n",
    "are necessarily finite samples.\n",
    "\n",
    "The alternative is an **analytic distribution**, which is characterized\n",
    "by a CDF that is a mathematical function. Analytic distributions can be\n",
    "used to model empirical distributions. In this context, a **model** is a\n",
    "simplification that leaves out unneeded details. This chapter presents\n",
    "common analytic distributions and uses them to model data from a variety\n",
    "of sources.\n",
    "\n",
    "The code for this chapter is in `analytic.py`. For information about\n",
    "downloading and working with this code, see\n",
    "Section [\\[code\\]](#code){reference-type=\"ref\" reference=\"code\"}."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "41ffa5f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from os.path import basename, exists\n",
    "\n",
    "\n",
    "def download(url):\n",
    "    filename = basename(url)\n",
    "    if not exists(filename):\n",
    "        from urllib.request import urlretrieve\n",
    "\n",
    "        local, _ = urlretrieve(url, filename)\n",
    "        print(\"Downloaded \" + local)\n",
    "\n",
    "\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/thinkstats2.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/thinkplot.py\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9fb94810",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import thinkstats2\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50b350db",
   "metadata": {},
   "source": [
    "## The exponential distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa0bab15",
   "metadata": {},
   "source": [
    "I'll start with the **exponential distribution** because it is\n",
    "relatively simple. The CDF of the exponential distribution is\n",
    "$$CDF(x) = 1 - e^{-\\lambda x}$$ The parameter, $\\lambda$, determines\n",
    "the shape of the distribution.\n",
    "\n",
    "Figure [\\[analytic_expo_cdf\\]](#analytic_expo_cdf){reference-type=\"ref\"\n",
    "reference=\"analytic_expo_cdf\"} shows what this CDF looks like with\n",
    "$\\lambda =$ 0.5, 1, and 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "571e2b78",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(3)\n",
    "for lam in [2.0, 1, 0.5]:\n",
    "    xs, ps = thinkstats2.RenderExpoCdf(lam, 0, 3.0, 50)\n",
    "    label = r\"$\\lambda=%g$\" % lam\n",
    "    thinkplot.Plot(xs, ps, label=label)\n",
    "\n",
    "thinkplot.Config(title=\"Exponential CDF\", xlabel=\"x\", ylabel=\"CDF\", loc=\"lower right\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "585cdd49",
   "metadata": {},
   "source": [
    "In the real world, exponential distributions come up when we look at a\n",
    "series of events and measure the times between events, called\n",
    "**interarrival times**. If the events are equally likely to occur at any\n",
    "time, the distribution of interarrival times tends to look like an\n",
    "exponential distribution.\n",
    "\n",
    "As an example, we will look at the interarrival time of births. On\n",
    "December 18, 1997, 44 babies were born in a hospital in Brisbane,\n",
    "Australia.[^1] The time of birth for all 44 babies was reported in the\n",
    "local paper; the complete dataset is in a file called `babyboom.dat`, in\n",
    "the `ThinkStats2` repository."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ad843bd3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloaded analytic.py\n",
      "Downloaded babyboom.dat\n"
     ]
    }
   ],
   "source": [
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/nsfg.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/analytic.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/babyboom.dat\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "50298fb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x600 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import analytic\n",
    "\n",
    "df = analytic.ReadBabyBoom()\n",
    "diffs = df.minutes.diff()\n",
    "cdf = thinkstats2.Cdf(diffs, label='actual')\n",
    "\n",
    "thinkplot.Cdf(cdf)\n",
    "thinkplot.Show(xlabel='minutes', ylabel='CDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bd6ac6e",
   "metadata": {},
   "source": [
    "`ReadBabyBoom` reads the data file and returns a DataFrame with columns\n",
    "`time`, `sex`, `weight_g`, and `minutes`, where `minutes` is time of\n",
    "birth converted to minutes since midnight.\n",
    "\n",
    "![CDF of interarrival times (left) and CCDF on a log-y scale\n",
    "(right).](figs/analytic_interarrivals.pdf){height=\"2.5in\"}\n",
    "\n",
    "`diffs` is the difference between consecutive birth times, and `cdf` is\n",
    "the distribution of these interarrival times.\n",
    "Figure [\\[analytic_interarrival_cdf\\]](#analytic_interarrival_cdf){reference-type=\"ref\"\n",
    "reference=\"analytic_interarrival_cdf\"} (left) shows the CDF. It seems to\n",
    "have the general shape of an exponential distribution, but how can we\n",
    "tell?\n",
    "\n",
    "One way is to plot the **complementary CDF**, which is $1 - CDF(x)$, on\n",
    "a log-y scale. For data from an exponential distribution, the result is\n",
    "a straight line. Let's see why that works.\n",
    "\n",
    "If you plot the complementary CDF (CCDF) of a dataset that you think is\n",
    "exponential, you expect to see a function like:\n",
    "$$y \\approx e^{-\\lambda x}$$ Taking the log of both sides yields:\n",
    "$$\\log y \\approx -\\lambda x$$ So on a log-y scale the CCDF is a straight\n",
    "line with slope $-\\lambda$. Here's how we can generate a plot like that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "aaaf89d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x600 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Cdf(cdf, complement=True)\n",
    "thinkplot.Show(xlabel='minutes',\n",
    "               ylabel='CCDF',\n",
    "               yscale='log')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bf0334d",
   "metadata": {},
   "source": [
    "With the argument `complement=True`, `thinkplot.Cdf` computes the\n",
    "complementary CDF before plotting. And with `yscale='log'`,\n",
    "`thinkplot.Show` sets the `y` axis to a logarithmic scale.\n",
    "\n",
    "Figure [\\[analytic_interarrival_cdf\\]](#analytic_interarrival_cdf){reference-type=\"ref\"\n",
    "reference=\"analytic_interarrival_cdf\"} (right) shows the result. It is\n",
    "not exactly straight, which indicates that the exponential distribution\n",
    "is not a perfect model for this data. Most likely the underlying\n",
    "assumption---that a birth is equally likely at any time of day---is not\n",
    "exactly true. Nevertheless, it might be reasonable to model this dataset\n",
    "with an exponential distribution. With that simplification, we can\n",
    "summarize the distribution with a single parameter.\n",
    "\n",
    "The parameter, $\\lambda$, can be interpreted as a rate; that is, the\n",
    "number of events that occur, on average, in a unit of time. In this\n",
    "example, 44 babies are born in 24 hours, so the rate is $\\lambda =\n",
    "0.0306$ births per minute. The mean of an exponential distribution is\n",
    "$1/\\lambda$, so the mean time between births is 32.7 minutes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85734123",
   "metadata": {},
   "source": [
    "## The normal distribution\n",
    "\n",
    "The **normal distribution**, also called Gaussian, is commonly used\n",
    "because it describes many phenomena, at least approximately. It turns\n",
    "out that there is a good reason for its ubiquity, which we will get to\n",
    "in Section [\\[CLT\\]](#CLT){reference-type=\"ref\" reference=\"CLT\"}."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26118498",
   "metadata": {},
   "source": [
    "The normal distribution is characterized by two parameters: the mean,\n",
    "$\\mu$, and standard deviation $\\sigma$. The normal distribution with\n",
    "$\\mu=0$ and $\\sigma=1$ is called the **standard normal distribution**.\n",
    "Its CDF is defined by an integral that does not have a closed form\n",
    "solution, but there are algorithms that evaluate it efficiently. One of\n",
    "them is provided by SciPy: `scipy.stats.norm` is an object that\n",
    "represents a normal distribution; it provides a method, `cdf`, that\n",
    "evaluates the standard normal CDF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "90141e7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats\n",
    "scipy.stats.norm.cdf(0)\n",
    "0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49cce37a",
   "metadata": {},
   "source": [
    "This result is correct: the median of the standard normal distribution\n",
    "is 0 (the same as the mean), and half of the values fall below the\n",
    "median, so $CDF(0)$ is 0.5.\n",
    "\n",
    "`norm.cdf` takes optional parameters: `loc`, which specifies the mean,\n",
    "and `scale`, which specifies the standard deviation.\n",
    "\n",
    "`thinkstats2` makes this function a little easier to use by providing\n",
    "`EvalNormalCdf`, which takes parameters `mu` and `sigma` and evaluates\n",
    "the CDF at `x`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f8b589a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def EvalNormalCdf(x, mu=0, sigma=1):\n",
    "    return scipy.stats.norm.cdf(x, loc=mu, scale=sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4819e11",
   "metadata": {},
   "source": [
    "Figure [\\[analytic_gaussian_cdf\\]](#analytic_gaussian_cdf){reference-type=\"ref\"\n",
    "reference=\"analytic_gaussian_cdf\"} shows CDFs for normal distributions\n",
    "with a range of parameters. The sigmoid shape of these curves is a\n",
    "recognizable characteristic of a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6fc8adae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(3)\n",
    "\n",
    "mus = [1.0, 2.0, 3.0]\n",
    "sigmas = [0.5, 0.4, 0.3]\n",
    "for mu, sigma in zip(mus, sigmas):\n",
    "    xs, ps = thinkstats2.RenderNormalCdf(mu=mu, sigma=sigma, low=-1.0, high=4.0)\n",
    "    label = r\"$\\mu=%g$, $\\sigma=%g$\" % (mu, sigma)\n",
    "    thinkplot.Plot(xs, ps, label=label)\n",
    "\n",
    "thinkplot.Config(title=\"Normal CDF\", xlabel=\"x\", ylabel=\"CDF\", loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5e0586f",
   "metadata": {},
   "source": [
    "In the previous chapter we looked at the distribution of birth weights\n",
    "in the NSFG.\n",
    "Figure [\\[analytic_birthwgt_model\\]](#analytic_birthwgt_model){reference-type=\"ref\"\n",
    "reference=\"analytic_birthwgt_model\"} shows the empirical CDF of weights\n",
    "for all live births and the CDF of a normal distribution with the same\n",
    "mean and variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5486a05a",
   "metadata": {},
   "outputs": [],
   "source": [
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/nsfg.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/first.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/2002FemPreg.dct\")\n",
    "download(\n",
    "    \"https://github.com/AllenDowney/ThinkStats2/raw/master/code/2002FemPreg.dat.gz\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8a65ba55",
   "metadata": {},
   "outputs": [],
   "source": [
    "import nsfg\n",
    "import first\n",
    "\n",
    "preg = nsfg.ReadFemPreg()\n",
    "weights = preg.totalwgt_lb.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6b1ecbb0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean, Var 7.280883100022579 1.5452125703544897\n",
      "Sigma 1.2430657948614343\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# estimate parameters: trimming outliers yields a better fit\n",
    "mu, var = thinkstats2.TrimmedMeanVar(weights, p=0.01)\n",
    "print(\"Mean, Var\", mu, var)\n",
    "\n",
    "# plot the model\n",
    "sigma = np.sqrt(var)\n",
    "print(\"Sigma\", sigma)\n",
    "xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=0, high=12.5)\n",
    "\n",
    "thinkplot.Plot(xs, ps, label=\"model\", color=\"0.6\")\n",
    "\n",
    "# plot the data\n",
    "cdf = thinkstats2.Cdf(weights, label=\"data\")\n",
    "\n",
    "thinkplot.PrePlot(1)\n",
    "thinkplot.Cdf(cdf)\n",
    "thinkplot.Config(title=\"Birth weights\", xlabel=\"Birth weight (pounds)\", ylabel=\"CDF\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d61e00da",
   "metadata": {},
   "source": [
    "The normal distribution is a good model for this dataset, so if we\n",
    "summarize the distribution with the parameters $\\mu = 7.28$ and\n",
    "$\\sigma = 1.24$, the resulting error (difference between the model and\n",
    "the data) is small.\n",
    "\n",
    "Below the 10th percentile there is a discrepancy between the data and\n",
    "the model; there are more light babies than we would expect in a normal\n",
    "distribution. If we are specifically interested in preterm babies, it\n",
    "would be important to get this part of the distribution right, so it\n",
    "might not be appropriate to use the normal model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0847a969",
   "metadata": {},
   "source": [
    "## Normal probability plot\n",
    "\n",
    "For the exponential distribution, and a few others, there are simple\n",
    "transformations we can use to test whether an analytic distribution is a\n",
    "good model for a dataset.\n",
    "\n",
    "For the normal distribution there is no such transformation, but there\n",
    "is an alternative called a **normal probability plot**. There are two\n",
    "ways to generate a normal probability plot: the hard way and the easy\n",
    "way. If you are interested in the hard way, you can read about it at\n",
    "<https://en.wikipedia.org/wiki/Normal_probability_plot>. Here's the easy\n",
    "way:\n",
    "\n",
    "1.  Sort the values in the sample.\n",
    "\n",
    "2.  From a standard normal distribution ($\\mu=0$ and $\\sigma=1$),\n",
    "    generate a random sample with the same size as the sample, and sort\n",
    "    it.\n",
    "\n",
    "3.  Plot the sorted values from the sample versus the random values.\n",
    "\n",
    "If the distribution of the sample is approximately normal, the result is\n",
    "a straight line with intercept `mu` and slope `sigma`. `thinkstats2`\n",
    "provides `NormalProbability`, which takes a sample and returns two NumPy\n",
    "arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e315f2dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "xs, ys = thinkstats2.NormalProbability(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b092cc6c",
   "metadata": {},
   "source": [
    "`ys` contains the sorted values from `sample`; `xs` contains the random\n",
    "values from the standard normal distribution.\n",
    "\n",
    "To test `NormalProbability` I generated some fake samples that were\n",
    "actually drawn from normal distributions with various parameters.\n",
    "Figure [\\[analytic_normal_prob_example\\]](#analytic_normal_prob_example){reference-type=\"ref\"\n",
    "reference=\"analytic_normal_prob_example\"} shows the results. The lines\n",
    "are approximately straight, with values in the tails deviating more than\n",
    "values near the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cdbf53bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 1000\n",
    "thinkplot.PrePlot(3)\n",
    "\n",
    "mus = [0, 1, 5]\n",
    "sigmas = [1, 1, 2]\n",
    "\n",
    "for mu, sigma in zip(mus, sigmas):\n",
    "    sample = np.random.normal(mu, sigma, n)\n",
    "    xs, ys = thinkstats2.NormalProbability(sample)\n",
    "    label = \"$\\mu=%d$, $\\sigma=%d$\" % (mu, sigma)\n",
    "    thinkplot.Plot(xs, ys, label=label)\n",
    "\n",
    "thinkplot.Config(\n",
    "    title=\"Normal probability plot\",\n",
    "    xlabel=\"standard normal sample\",\n",
    "    ylabel=\"sample values\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d5bdbfb",
   "metadata": {},
   "source": [
    "Now let's try it with real data. Here's code to generate a normal\n",
    "probability plot for the birth weight data from the previous section. It\n",
    "plots a gray line that represents the model and a blue line that\n",
    "represents the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "37d261a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeNormalPlot(weights):\n",
    "    mean = weights.mean()\n",
    "    std = weights.std()\n",
    "\n",
    "    xs = [-4, 4]\n",
    "    fxs, fys = thinkstats2.FitLine(xs, inter=mean, slope=std)\n",
    "    thinkplot.Plot(fxs, fys, color='gray', label='model')\n",
    "\n",
    "    xs, ys = thinkstats2.NormalProbability(weights)\n",
    "    thinkplot.Plot(xs, ys, label='birth weights')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8695eca",
   "metadata": {},
   "source": [
    "`weights` is a pandas Series of birth weights; `mean` and `std` are the\n",
    "mean and standard deviation.\n",
    "\n",
    "`FitLine` takes a sequence of `xs`, an intercept, and a slope; it\n",
    "returns `xs` and `ys` that represent a line with the given parameters,\n",
    "evaluated at the values in `xs`.\n",
    "\n",
    "`NormalProbability` returns `xs` and `ys` that contain values from the\n",
    "standard normal distribution and values from `weights`. If the\n",
    "distribution of weights is normal, the data should match the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3799bae7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean, var = thinkstats2.TrimmedMeanVar(weights, p=0.01)\n",
    "std = np.sqrt(var)\n",
    "\n",
    "xs = [-4, 4]\n",
    "fxs, fys = thinkstats2.FitLine(xs, mean, std)\n",
    "thinkplot.Plot(fxs, fys, linewidth=4, color=\"0.8\")\n",
    "\n",
    "xs, ys = thinkstats2.NormalProbability(weights)\n",
    "thinkplot.Plot(xs, ys, label=\"all live\")\n",
    "\n",
    "thinkplot.Config(\n",
    "    title=\"Normal probability plot\",\n",
    "    xlabel=\"Standard deviations from mean\",\n",
    "    ylabel=\"Birth weight (lbs)\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "721d5bc0",
   "metadata": {},
   "source": [
    "Figure [\\[analytic_birthwgt_normal\\]](#analytic_birthwgt_normal){reference-type=\"ref\"\n",
    "reference=\"analytic_birthwgt_normal\"} shows the results for all live\n",
    "births, and also for full term births (pregnancy length greater than 36\n",
    "weeks). Both curves match the model near the mean and deviate in the\n",
    "tails. The heaviest babies are heavier than what the model expects, and\n",
    "the lightest babies are lighter.\n",
    "\n",
    "When we select only full term births, we remove some of the lightest\n",
    "weights, which reduces the discrepancy in the lower tail of the\n",
    "distribution.\n",
    "\n",
    "This plot suggests that the normal model describes the distribution well\n",
    "within a few standard deviations from the mean, but not in the tails.\n",
    "Whether it is good enough for practical purposes depends on the\n",
    "purposes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0690e053",
   "metadata": {},
   "source": [
    "## The lognormal distribution\n",
    "\n",
    "If the logarithms of a set of values have a normal distribution, the\n",
    "values have a **lognormal distribution**. The CDF of the lognormal\n",
    "distribution is the same as the CDF of the normal distribution, with\n",
    "$\\log x$ substituted for $x$.\n",
    "$$CDF_{lognormal}(x) = CDF_{normal}(\\log x)$$ The parameters of the\n",
    "lognormal distribution are usually denoted $\\mu$ and $\\sigma$. But\n",
    "remember that these parameters are *not* the mean and standard\n",
    "deviation; the mean of a lognormal distribution is\n",
    "$\\exp(\\mu +\\sigma^2/2)$ and the standard deviation is ugly (see\n",
    "<http://wikipedia.org/wiki/Log-normal_distribution>)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b92b002",
   "metadata": {},
   "source": [
    "If a sample is approximately lognormal and you plot its CDF on a log-x\n",
    "scale, it will have the characteristic shape of a normal distribution.\n",
    "To test how well the sample fits a lognormal model, you can make a\n",
    "normal probability plot using the log of the values in the sample.\n",
    "\n",
    "As an example, let's look at the distribution of adult weights, which is\n",
    "approximately lognormal.[^2]\n",
    "\n",
    "The National Center for Chronic Disease Prevention and Health Promotion\n",
    "conducts an annual survey as part of the Behavioral Risk Factor\n",
    "Surveillance System (BRFSS).[^3] In 2008, they interviewed 414,509\n",
    "respondents and asked about their demographics, health, and health\n",
    "risks. Among the data they collected are the weights in kilograms of\n",
    "398,484 respondents.\n",
    "\n",
    "The repository for this book contains `CDBRFS08.ASC.gz`, a fixed-width\n",
    "ASCII file that contains data from the BRFSS, and `brfss.py`, which\n",
    "reads the file and analyzes the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d80d103c",
   "metadata": {},
   "outputs": [],
   "source": [
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/brfss.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/CDBRFS08.ASC.gz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7ea83cdd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import brfss\n",
    "\n",
    "df = brfss.ReadBrfss()\n",
    "weights = df.wtkg2.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c606acc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeNormalModel(weights):\n",
    "    \"\"\"Plots a CDF with a Normal model.\n",
    "\n",
    "    weights: sequence\n",
    "    \"\"\"\n",
    "    cdf = thinkstats2.Cdf(weights, label=\"weights\")\n",
    "\n",
    "    mean, var = thinkstats2.TrimmedMeanVar(weights)\n",
    "    std = np.sqrt(var)\n",
    "    print(\"n, mean, std\", len(weights), mean, std)\n",
    "\n",
    "    xmin = mean - 4 * std\n",
    "    xmax = mean + 4 * std\n",
    "\n",
    "    xs, ps = thinkstats2.RenderNormalCdf(mean, std, xmin, xmax)\n",
    "    thinkplot.Plot(xs, ps, label=\"model\", linewidth=4, color=\"0.8\")\n",
    "    thinkplot.Cdf(cdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d6c83844",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n, mean, std 9038 7.280883100022579 1.2430657948614343\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MakeNormalModel(weights)\n",
    "thinkplot.Config(\n",
    "    title=\"Adult weight, linear scale\",\n",
    "    xlabel=\"Weight (kg)\",\n",
    "    ylabel=\"CDF\",\n",
    "    loc=\"upper right\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2059a4bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n, mean, std 9038 0.8550971035123834 0.08132700287556055\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_weights = np.log10(weights)\n",
    "MakeNormalModel(log_weights)\n",
    "thinkplot.Config(\n",
    "    title=\"Adult weight, log scale\",\n",
    "    xlabel=\"Weight (log10 kg)\",\n",
    "    ylabel=\"CDF\",\n",
    "    loc=\"upper right\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec523cbc",
   "metadata": {},
   "source": [
    "Figure [\\[brfss_weight\\]](#brfss_weight){reference-type=\"ref\"\n",
    "reference=\"brfss_weight\"} (left) shows the distribution of adult weights\n",
    "on a linear scale with a normal model.\n",
    "Figure [\\[brfss_weight\\]](#brfss_weight){reference-type=\"ref\"\n",
    "reference=\"brfss_weight\"} (right) shows the same distribution on a log\n",
    "scale with a lognormal model. The lognormal model is a better fit, but\n",
    "this representation of the data does not make the difference\n",
    "particularly dramatic.\n",
    "\n",
    "Figure [\\[brfss_weight_normal\\]](#brfss_weight_normal){reference-type=\"ref\"\n",
    "reference=\"brfss_weight_normal\"} shows normal probability plots for\n",
    "adult weights, $w$, and for their logarithms, $\\log_{10} w$. Now it is\n",
    "apparent that the data deviate substantially from the normal model. On\n",
    "the other hand, the lognormal model is a good match for the data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecaa5709",
   "metadata": {},
   "source": [
    "## The Pareto distribution\n",
    "\n",
    "The **Pareto distribution** is named after the economist Vilfredo\n",
    "Pareto, who used it to describe the distribution of wealth (see\n",
    "<http://wikipedia.org/wiki/Pareto_distribution>). Since then, it has\n",
    "been used to describe phenomena in the natural and social sciences\n",
    "including sizes of cities and towns, sand particles and meteorites,\n",
    "forest fires and earthquakes.\n",
    "\n",
    "The CDF of the Pareto distribution is:\n",
    "$$CDF(x) = 1 - \\left( \\frac{x}{x_m} \\right) ^{-\\alpha}$$ The parameters\n",
    "$x_{m}$ and $\\alpha$ determine the location and shape of the\n",
    "distribution. $x_{m}$ is the minimum possible value.\n",
    "Figure [\\[analytic_pareto_cdf\\]](#analytic_pareto_cdf){reference-type=\"ref\"\n",
    "reference=\"analytic_pareto_cdf\"} shows CDFs of Pareto distributions with\n",
    "$x_{m} = 0.5$ and different values of $\\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e559282f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xmin = 0.5\n",
    "\n",
    "thinkplot.PrePlot(3)\n",
    "for alpha in [2.0, 1.0, 0.5]:\n",
    "    xs, ps = thinkstats2.RenderParetoCdf(xmin, alpha, 0, 10.0, n=100)\n",
    "    thinkplot.Plot(xs, ps, label=r\"$\\alpha=%g$\" % alpha)\n",
    "\n",
    "thinkplot.Config(title=\"Pareto CDF\", xlabel=\"x\", ylabel=\"CDF\", loc=\"lower right\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4360eee",
   "metadata": {},
   "source": [
    "There is a simple visual test that indicates whether an empirical\n",
    "distribution fits a Pareto distribution: on a log-log scale, the CCDF\n",
    "looks like a straight line. Let's see why that works.\n",
    "\n",
    "If you plot the CCDF of a sample from a Pareto distribution on a linear\n",
    "scale, you expect to see a function like:\n",
    "$$y \\approx \\left( \\frac{x}{x_m} \\right) ^{-\\alpha}$$ Taking the log of\n",
    "both sides yields: $$\\log y \\approx -\\alpha (\\log x - \\log x_{m})$$ So\n",
    "if you plot $\\log y$ versus $\\log x$, it should look like a straight\n",
    "line with slope $-\\alpha$ and intercept $\\alpha \\log x_{m}$.\n",
    "\n",
    "As an example, let's look at the sizes of cities and towns. The\n",
    "U.S. Census Bureau publishes the population of every incorporated city\n",
    "and town in the United States."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9f1ede9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloaded populations.py\n",
      "Downloaded PEP_2012_PEPANNRES_with_ann.csv\n"
     ]
    }
   ],
   "source": [
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/populations.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/PEP_2012_PEPANNRES_with_ann.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "18929b3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of cities/towns 19515\n"
     ]
    }
   ],
   "source": [
    "import populations\n",
    "\n",
    "pops = populations.ReadData()\n",
    "print(\"Number of cities/towns\", len(pops))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07f5b5e7",
   "metadata": {},
   "source": [
    "I downloaded their data from\n",
    "<http://www.census.gov/popest/data/cities/totals/2012/SUB-EST2012-3.html>;\n",
    "it is in the repository for this book in a file named\n",
    "`PEP_2012_PEPANNRES_with_ann.csv`. The repository also contains\n",
    "`populations.py`, which reads the file and plots the distribution of\n",
    "populations.\n",
    "\n",
    "Figure [\\[populations_pareto\\]](#populations_pareto){reference-type=\"ref\"\n",
    "reference=\"populations_pareto\"} shows the CCDF of populations on a\n",
    "log-log scale. The largest 1% of cities and towns, below $10^{-2}$, fall\n",
    "along a straight line. So we could conclude, as some researchers have,\n",
    "that the tail of this distribution fits a Pareto model.\n",
    "\n",
    "On the other hand, a lognormal distribution also models the data well.\n",
    "Figure [\\[populations_normal\\]](#populations_normal){reference-type=\"ref\"\n",
    "reference=\"populations_normal\"} shows the CDF of populations and a\n",
    "lognormal model (left), and a normal probability plot (right). Both\n",
    "plots show good agreement between the data and the model.\n",
    "\n",
    "Neither model is perfect. The Pareto model only applies to the largest\n",
    "1% of cities, but it is a better fit for that part of the distribution.\n",
    "The lognormal model is a better fit for the other 99%. Which model is\n",
    "appropriate depends on which part of the distribution is relevant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ad635d57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_pops = np.log10(pops)\n",
    "cdf = thinkstats2.Cdf(pops, label=\"data\")\n",
    "cdf_log = thinkstats2.Cdf(log_pops, label=\"data\")\n",
    "\n",
    "# pareto plot\n",
    "xs, ys = thinkstats2.RenderParetoCdf(xmin=5000, alpha=1.4, low=0, high=1e7)\n",
    "thinkplot.Plot(np.log10(xs), 1 - ys, label=\"model\", color=\"0.8\")\n",
    "\n",
    "thinkplot.Cdf(cdf_log, complement=True)\n",
    "thinkplot.Config(\n",
    "    xlabel=\"log10 population\", ylabel=\"CCDF\", yscale=\"log\", loc=\"lower left\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "6df10305",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(cols=2)\n",
    "\n",
    "mu, sigma = log_pops.mean(), log_pops.std()\n",
    "xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=0, high=8)\n",
    "thinkplot.Plot(xs, ps, label=\"model\", color=\"0.8\")\n",
    "\n",
    "thinkplot.Cdf(cdf_log)\n",
    "thinkplot.Config(xlabel=\"log10 population\", ylabel=\"CDF\", loc=\"lower right\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8be0f092",
   "metadata": {},
   "source": [
    "## Generating random numbers\n",
    "\n",
    "Analytic CDFs can be used to generate random numbers with a given\n",
    "distribution function, $p = CDF(x)$. If there is an efficient way to\n",
    "compute the inverse CDF, we can generate random values with the\n",
    "appropriate distribution by choosing $p$ from a uniform distribution\n",
    "between 0 and 1, then choosing $x = ICDF(p)$.\n",
    "\n",
    "For example, the CDF of the exponential distribution is\n",
    "$$p = 1 - e^{-\\lambda x}$$ Solving for $x$ yields:\n",
    "$$x = -\\log (1 - p) / \\lambda$$ So in Python we can write"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "3295e3ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def expovariate(lam):\n",
    "    p = random.random()\n",
    "    x = -np.log(1-p) / lam\n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bbbce62",
   "metadata": {},
   "source": [
    "`expovariate` takes `lam` and returns a random value chosen from the\n",
    "exponential distribution with parameter `lam`.\n",
    "\n",
    "Two notes about this implementation: I called the parameter `lam`\n",
    "because `lambda` is a Python keyword. Also, since $\\log 0$ is undefined,\n",
    "we have to be a little careful. The implementation of `random.random`\n",
    "can return 0 but not 1, so $1 - p$ can be 1 but not 0, so `log(1-p)` is\n",
    "always defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b823e8ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = [expovariate(lam=2) for _ in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2b671e3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf = thinkstats2.Cdf(t)\n",
    "\n",
    "thinkplot.Cdf(cdf, complement=True)\n",
    "thinkplot.Config(xlabel=\"Exponential variate\", ylabel=\"CCDF\", yscale=\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "710eb305",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "0f46ee83",
   "metadata": {},
   "source": [
    "## Why model?\n",
    "\n",
    "At the beginning of this chapter, I said that many real world phenomena\n",
    "can be modeled with analytic distributions. \"So,\" you might ask, \"what?\"\n",
    "\n",
    "Like all models, analytic distributions are abstractions, which means\n",
    "they leave out details that are considered irrelevant. For example, an\n",
    "observed distribution might have measurement errors or quirks that are\n",
    "specific to the sample; analytic models smooth out these idiosyncrasies.\n",
    "\n",
    "Analytic models are also a form of data compression. When a model fits a\n",
    "dataset well, a small set of parameters can summarize a large amount of\n",
    "data.\n",
    "\n",
    "It is sometimes surprising when data from a natural phenomenon fit an\n",
    "analytic distribution, but these observations can provide insight into\n",
    "physical systems. Sometimes we can explain why an observed distribution\n",
    "has a particular form. For example, Pareto distributions are often the\n",
    "result of generative processes with positive feedback (so-called\n",
    "preferential attachment processes: see\n",
    "<http://wikipedia.org/wiki/Preferential_attachment>.)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "439331ea",
   "metadata": {},
   "source": [
    "Also, analytic distributions lend themselves to mathematical analysis,\n",
    "as we will see in Chapter [\\[analysis\\]](#analysis){reference-type=\"ref\"\n",
    "reference=\"analysis\"}.\n",
    "\n",
    "But it is important to remember that all models are imperfect. Data from\n",
    "the real world never fit an analytic distribution perfectly. People\n",
    "sometimes talk as if data are generated by models; for example, they\n",
    "might say that the distribution of human heights is normal, or the\n",
    "distribution of income is lognormal. Taken literally, these claims\n",
    "cannot be true; there are always differences between the real world and\n",
    "mathematical models.\n",
    "\n",
    "Models are useful if they capture the relevant aspects of the real world\n",
    "and leave out unneeded details. But what is \"relevant\" or \"unneeded\"\n",
    "depends on what you are planning to use the model for."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51b53d8c",
   "metadata": {},
   "source": [
    "A straight line is consistent with an exponential distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70f3aa6e",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61517a44",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** Write a function that generates a Pareto variate. Generate a sample and plot its complementary CDF on a log-log scale. Does it look like a straight line?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "beedf20a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "\n",
    "def sample_pareto(alpha, x_m, size):\n",
    "    u = np.random.random(size)\n",
    "    return x_m * pow(1 - u, -1 / alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "804a0e61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "sample = sample_pareto(1, 2, 1000)\n",
    "cdf = thinkstats2.Cdf(sample)\n",
    "\n",
    "thinkplot.Cdf(cdf, complement=True)\n",
    "thinkplot.Config(xlabel=\"Random values\", ylabel=\"CCDF\", xscale=\"log\", yscale=\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b94c27ad",
   "metadata": {},
   "source": [
    "**Exercise:** In the BRFSS (see Section 5.4), the distribution of heights is roughly normal with parameters µ = 178 cm and σ = 7.7 cm for men, and µ = 163 cm and σ = 7.3 cm for women.\n",
    "\n",
    "In order to join Blue Man Group, you have to be male between 5’10” and 6’1” (see http://bluemancasting.com). What percentage of the U.S. male population is in this range? Hint: use `scipy.stats.norm.cdf`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcbf98a7",
   "metadata": {},
   "source": [
    "`scipy.stats` contains objects that represent analytic distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "fb20ec1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7427bcf9",
   "metadata": {},
   "source": [
    "For example <tt>scipy.stats.norm</tt> represents a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "5822d6bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "scipy.stats._distn_infrastructure.rv_continuous_frozen"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu = 178\n",
    "sigma = 7.7\n",
    "dist = scipy.stats.norm(loc=mu, scale=sigma)\n",
    "type(dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a08ac2c9",
   "metadata": {},
   "source": [
    "A \"frozen random variable\" can compute its mean and standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "004a9632",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(178.0, 7.7)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist.mean(), dist.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2184747",
   "metadata": {},
   "source": [
    "It can also evaluate its CDF.  How many people are below the mean by more than one standard deviation?  About 16%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "23061ba2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1586552539314574"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist.cdf(mu - sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "563681fa",
   "metadata": {},
   "source": [
    "How many people are between 5'10\" and 6'1\"?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "f295ffc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.48963902786483265, 0.8317337108107857, 0.3420946829459531)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "low = dist.cdf(177.8)  # 5'10\"\n",
    "high = dist.cdf(185.4)  # 6'1\"\n",
    "low, high, high - low"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8d839c1",
   "metadata": {},
   "source": [
    "**Exercise:** To get a feel for the Pareto distribution, let’s see how different the world would be if the distribution of human height were Pareto. With the parameters xm = 1 m and α = 1.7, we get a distribution with a reasonable minimum, 1 m, and median, 1.5 m.\n",
    "\n",
    "Plot this distribution. What is the mean human height in Pareto world? What fraction of the population is shorter than the mean? If there are 7 billion people in Pareto world, how many do we expect to be taller than 1 km? How tall do we expect the tallest person to be?\n",
    "\n",
    "`scipy.stats.pareto` represents a pareto distribution.  In Pareto world, the distribution of human heights has parameters alpha=1.7 and xmin=1 meter.  So the shortest person is 100 cm and the median is 150."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "b7f180dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5034066538560549"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = 1.7\n",
    "xmin = 1  # meter\n",
    "dist = scipy.stats.pareto(b=alpha, scale=xmin)\n",
    "dist.median()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2cd55ea",
   "metadata": {},
   "source": [
    "What is the mean height in Pareto world?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4d6c3f98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.428571428571429"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "dist.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59cb3e1d",
   "metadata": {},
   "source": [
    "What fraction of people are shorter than the mean?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "96491bae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.778739697565288"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "dist.cdf(dist.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1baadb33",
   "metadata": {},
   "source": [
    "Out of 7 billion people, how many do we expect to be taller than 1 km?  You could use <tt>dist.cdf</tt> or <tt>dist.sf</tt>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "689b2a73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(55602.976430479954, 55602.97643069972)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "(1 - dist.cdf(1000)) * 7e9, dist.sf(1000) * 7e9"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a15aa58",
   "metadata": {},
   "source": [
    "How tall do we expect the tallest person to be?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "d4c41e5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0525455861201714"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# One way to solve this is to search for a height that we\n",
    "# expect one person out of 7 billion to exceed.\n",
    "\n",
    "# It comes in at roughly 600 kilometers.\n",
    "\n",
    "dist.sf(600000) * 7e9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "e8f4c5fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "618349.6106759505"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Another way is to use `ppf`, which evaluates the \"percent point function\", which\n",
    "# is the inverse CDF.  So we can compute the height in meters that corresponds to\n",
    "# the probability (1 - 1/7e9).\n",
    "\n",
    "dist.ppf(1 - 1 / 7e9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "235c3943",
   "metadata": {},
   "source": [
    "**Exercise:** The Weibull distribution is a generalization of the exponential distribution that comes up in failure analysis (see http://wikipedia.org/wiki/Weibull_distribution). Its CDF is\n",
    "\n",
    "$\\mathrm{CDF}(x) = 1 − \\exp[−(x / λ)^k]$ \n",
    "\n",
    "Can you find a transformation that makes a Weibull distribution look like a straight line? What do the slope and intercept of the line indicate?\n",
    "\n",
    "Use `random.weibullvariate` to generate a sample from a Weibull distribution and use it to test your transformation.\n",
    "\n",
    "Generate a sample from a Weibull distribution and plot it using a transform that makes a Weibull distribution look like a straight line."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb527fb9",
   "metadata": {},
   "source": [
    "If you are stuck, you can get a hint from `thinkplot.Cdf`, which provides a transform that makes the CDF of a Weibull distribution look like a straight line.  Here's an example that shows how it's used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9e2083fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample = [random.weibullvariate(2, 1) for _ in range(1000)]\n",
    "cdf = thinkstats2.Cdf(sample)\n",
    "thinkplot.Cdf(cdf, transform=\"weibull\")\n",
    "thinkplot.Config(xlabel=\"Weibull variate\", ylabel=\"CCDF\", \n",
    "                 xscale=\"log\", yscale=\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cdfaaec",
   "metadata": {},
   "source": [
    "**Exercise:** For small values of `n`, we don’t expect an empirical distribution to fit an analytic distribution exactly. One way to evaluate the quality of fit is to generate a sample from an analytic distribution and see how well it matches the data.\n",
    "\n",
    "For example, in Section 5.1 we plotted the distribution of time between births and saw that it is approximately exponential. But the distribution is based on only 44 data points. To see whether the data might have come from an exponential distribution, generate 44 values from an exponential distribution with the same mean as the data, about 33 minutes between births.\n",
    "\n",
    "Plot the distribution of the random values and compare it to the actual distribution. You can use random.expovariate to generate the values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "9955fd76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32.72727272727273, 28.768326594024213)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import analytic\n",
    "\n",
    "df = analytic.ReadBabyBoom()\n",
    "diffs = df.minutes.diff()\n",
    "cdf = thinkstats2.Cdf(diffs, label=\"actual\")\n",
    "\n",
    "n = len(diffs)\n",
    "lam = 44.0 / 24 / 60\n",
    "sample = [random.expovariate(lam) for _ in range(n)]\n",
    "\n",
    "1 / lam, np.mean(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "9dacaba8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qLKsM+Wr03EEGANbCpTGE3Knrj0U77RrdO1kZaYlBfc6qO9CKy6qPNaq6gywYl98AAE0LPUJoUkor3Fq45UjQe4a4Aw0AINEjhEYW43Qo2mlXaUXNl55KK9x+3UlWX7Ut3QEAsAZ6hNCoHHabRvdOVrSzafzTq2npDgCANdAjhEaXkZaoPqkJKqlwSTo5WPrUcUJV26rEOB1y2G2NWiMAwBoIQggJh91W66WvUAygBgBYT9O4PgHUorEGUAMArIcghJCrGkBdm6oB1AAABBJBCCHX1AZQAwCsgzFCaBLqMoC6MbHuGABYA0EITcaZBlA3pmlzVyk2KkK3jOihzPTUUJcDAAgSvu4ibJy6JlljrEvGumMA0Pw1ja/fQB2cfqksULfVs+4YAFgXPUIIW4G6rZ51xwDAunjnR5NUlzXJpMCtS8a6YwBgTfQIoUkKxS31Na07VlBSrvyikz+MFwKA5oUeITRZp99SL4XmtvpTe4i4kwwAmheCEJq0utxSf+oCrf7yd0HXqjvJLuqVwhxDANAMEIQQ9hrSQ3T6nWe13UFWhTvJAKD54CutD9nZ2erVq5cGDhwY6lIQZKffecYdZABgLbzb+5CVlaWsrCwVFBQoMbFhc9QgsOp6N5k/Tr/zrOoOssLSk71CBSXl3EkGAM0UPUIIK411N5nDYVdiXKQS4yJ93kkGAGge6BFC2PF1N5k/AnHnWUFJuV/Hs4ArADRNBCGEpVAv0OrvpTJuuweApomvqIC8F3QNxmKuLOAKAE0TPUKAvG/Br88t9XXBbfcA0PTQIwSchlvqAcA6eGeH5dTlFvwz3VJfF9x2DwBNH0EIllN1C/7CLUf8mo+o6pZ6AEDzQRCCJZ1+C34oFnMFAIQeQQiWFYpb8E+ff4j5hQAgtAhCQCM6fcwQ8wsBQGjxVRSoQXG5KyhzCnk9B/MLAUBI0SME1ODp5bnV5hTyR13nH2J+IQAIHXqEgFqcPqeQP5h/CACaPt6hAdU+t9Dpcwr5w9f8Q8wvBABNBz1CgH6cWyjaGfj/ElXzD1X9JMRwCQwAmgp6hID/qJpb6PuicuYUAgCLIAgBp3DYbYqNdDT6854+v1B9MCcRAPiPIAQ0AYEYM8ScRADgP74+As0EcxIBgP8IQkAdbD5QELBzVc0vFAxVcxIBAOqGIATUwQdb8wI2yzTzCwFA08E7MXCaGKfvwdL1nUvIF1/zC9UHcxIBQMMQhIDTOOw2XX5ekj7Ymhfc5/nP/EIAgNDh0hjgQ98OCaEuAQDQCAhCAADAsghCAADAsghCQDNTUFLOXEIAUEcMlgaamWlzVzHLNADUEUEIqKPiclfAzhXjdMhhtwXsfKermmX6ol4prD8GALUgCAF1FMgV6aOddo3unayMtMQGnadqlurisurzEVXNMs0t+gBQM74qAiFQWuHWwi1HGjxbNbNUA0DD8O4J+BDjdCjaaVdpRfAGHZdWuAMyW3XVLNUHjxUzyzQA+IkeIcAHh92m0b2TFe0Mj/8iDoddCTFcAgMAf9Ej5EN2drays7PlcgVucCzCT0ZaovqkJqikIjD/DorLXQEdZwQAaDiCkA9ZWVnKyspSQUGBEhMbNpgV4c1htwVsoVUAQNMTHv3+AAAAQcBXXaAZKygpP+Mx8dERzDUEwLIIQkAzVpe7yJiFGoCV8TUQsLiqWahZnwyAFRGEgGaiapbp+qiahRoArIYgBDQTzDINAP7jHRNoRqpmmT5T705BSTmzUAOA/OwReumll1RWVhasWgAEgMNhV2JcZK0/zEINACf5FYQmTZqk/Px8z+PU1FR98803ga4JAACgUfgVhIzxXin7xIkTcru50wQAAIQnBksDAADL8isI2Ww22Wy2Gh8DAACEE7/uGjPGqHv37p7wU1hYqIyMDNnt3nnqhx9+CFyFAAAAQeJXEJo3b16w6gAQYqeuS8b6YwCswq8gNH78+GDVASDETp1XiPXHAFhFvSZUNMZo/fr1+uabb2Sz2dSlSxdlZGQwXgjwU3G5q07HxTgdctgb7/9X1fpjF/VKoWcIQLPmdxBatmyZfv3rX2vv3r2e2+mrwtBLL72kn/zkJwEvEmiunl6eW6fjop12je6drIy0xIA8b9W6ZMVlNc9AXbX+WGIcky8CaL78+qq3e/dujR49Wp07d9aCBQu0bds25eTk6M0331RaWpouv/xyff3118GqFbCs0gq3Fm45IpfbnPngOmBdMgA4ya93wTlz5mjIkCFaunSp1/YePXpozJgxGj58uP785z/r2WefDWiRQHMQ43Qo2mlXaUX9JiEtrXCrpMKl+ACFl9PXJWP9MQBW5FeP0PLlyzVt2jSf+2w2m6ZNm6Zly5YFoi6g2XHYbRrdO1nRzqYz5ubUdclYfwyAFfn11XLfvn1KT0+vcX/v3r21d+/eBhcFNFcZaYnqk5qgkoozD5IuLnfVeQwRAKB+/ApChYWFio2NrXF/bGysiouLG1wU0Jw57LaAXd4CADSM3+/GOTk5Onz4sM99R48ebXBBAAAAjcXvIHTppZdWW4VeOjlGyBjDXEIAACBs+BWEcnMZrwAAAJoPv4LQWWedFaw6AAAAGp1f9/Hu2rVLN9xwgwoKCqrty8/P14033siEigAAIGz4FYSeeOIJdezYUQkJCdX2JSYmqmPHjnriiScCVhyA0CooKZfLVb8JIAEgHPgVhFasWKGf/exnNe7/+c9/rk8++aTBRQFoGqbNXaWb5yzXiq8OhroUAAgKv4LQvn37lJSUVOP+tm3bav/+/Q0uCoBvbh93bAZb1Ur09AwBaI78CkKJiYnas2dPjft3797t87IZgMCYvWSPNn6bH5RzV61I70vVSvQA0Nz4FYR+8pOf1Lqg6jPPPKOLL764wUUBqFkgV6E/FSvSA7Aiv97xZs6cqaFDh+r666/XH/7wB5177rmSpO3bt+vxxx/XokWLtGoVq1cDgVDTavWBXoX+VFUr0h88VsxK9AAswa930oyMDL311luaOHGi3n77ba99bdq00RtvvKHzzz8/oAUCVlW1Wv1bGw817vM67KxED8Ay/P5KOXr0aO3du1cfffSRdu/eLWOMunfvrhEjRtS6ICsA/2WkJeqctrGavaTmsXkAgPrzKwh98sknmjJlij7//HONGTPGa19+fr7OO+88Pf/884wTAgLIzvp9ABA0fg2WnjNnjiZNmlTjhIq/+c1v9NRTTwWsOAAAgGDyKwht3rxZl112WY37R4wYofXr1ze4KAAAgMbgVxA6cuSInE5njfsjIiL03XffNbgoAACAxuBXEOrQoYO2bNlS4/4vv/xS7du3b3BRAAAAjcGvIHT55Zfr3nvvVWlpabV9JSUluv/++zV69OiAFQcAABBMft01ds8992jBggXq3r27pkyZ4jWhYnZ2tlwul/70pz8FpVAAAIBA8ysIJScna9WqVZo8ebJmzpwp858FIG02m0aOHKns7GwlJycHpVAAAIBA83tCxbPOOksffPCBjh075plQsVu3bmrVqlUw6gPQRBSUlNf7d+OjI+Rw+HUlHgAaRb0XK2rVqpUGDhwYyFoANGENWXssNipCt4zoocz01ABWBAANx1c0IAwVl7tUWFYZlFXog6G4rFIvLt4ul8t95oMBoBEFfvlqAEH39PJcSVK0067RvZOVkZYY0PPHR0coNipCxWWVATtncVmlCksrlRjHgq4Amg56hIAwVlrh1sItRwLeM+Rw2HXLiB6KjeK7EoDmjXc5oImLcToU7bSrtML3ZaXSCrdKKlyKD3BoyUxP1UW9UlRYWr9eoYKS8gaNKwKAxkAQApo4h92m0b2TtXDLkRrDUNCe22HnUhaAZo0gBISBjLRE9UlNUEmFS8XlLs8YIQBAwxCEgDDhsNsCfvkLAKyOwdIAAMCyCEIAAMCyLBGExowZo1atWun6668PdSkAAKAJsUQQmjp1qv7+97+HugwAANDEWCIIDRs2TC1atAh1GQAAoIkJeRBauXKlrrzySqWmpspms+mdd96pdkx2drY6d+6s6OhoDR48WGvWrGn8QgEAQLMT8ntxi4qK1LdvX02cOFHXXntttf2vv/66pk+frueff16DBw/WnDlzNHLkSO3YsUNJSUmSpH79+qmysvrst4sXL1Zqat1Xuy4rK1NZWZnncUFBQT1aBAAAwkXIg9CoUaM0atSoGvc/9dRTmjRpkiZMmCBJev755/X+++/rpZde0h//+EdJ0qZNmwJSy6xZs/Tggw8G5FwAAKDpC/mlsdqUl5dr/fr1Gj58uGeb3W7X8OHDtXr16oA/38yZM5Wfn+/52b9/f8CfAwAANB0h7xGqzdGjR+VyuZScnOy1PTk5Wdu3b6/zeYYPH67NmzerqKhIaWlpevPNNzV06NBqx0VFRSkqKqrBdQMAgPDQpINQoHz88cehLgEAADRBTToItW3bVg6HQ0eOHPHafuTIEaWkpISoKgD1VVBS7vlzfHSEHI4mfXUegAU06SAUGRmp/v37a+nSpbrmmmskSW63W0uXLtWUKVNCWxwAv02bu8rz59ioCN0yoocy0+t+ZycABFrIg1BhYaF2797teZybm6tNmzapdevW6tSpk6ZPn67x48drwIABGjRokObMmaOioiLPXWQApOJyV6hLqKao3CVT2/6ySs1dvF0Z57SV3Y+eoRinQw67reEFAoCaQBBat26dLrnkEs/j6dOnS5LGjx+v+fPna+zYsfruu+9033336fDhw+rXr58++uijagOoASt7enluqEuoxhij0rhYudw1x6EiSY8s3q0IP4JQtNOu0b2TlZGWGIAqAVidzRhT25c2SysoKFBiYqLy8/OVkJAQ6nIASVJhWaVmLd595gObgO9PlGrfd4W1hqF+Xdr4FYSkk2Ho7hHd6BkC4JM/n98h7xEC4J8Yp0PRTrtKK9yhLuWM2rSIVuv4KE8QqnC5tXXfsQaft7TCrZIKl+KjeAsD0DDcsuFDdna2evXqpYEDB4a6FKAah92m0b2TFe0Mj/++NptNEQ67Ihx2OblLDEATw6WxWnBpDE2Zy21UUtH0BknXpqC4QlOe+7fXtr9MvlgJsc5af6+43FVtHNTMEV3pEQLgE5fGAAtw2G1hFwRclW6dPqonLtIRdu0A0HzQTw0AACyLIAQAACyLIAQAACyLIAQAACyLIAQAACyLIAQAACyLIAQAACyLIOQDM0sDAGANBCEfsrKylJOTo7Vr14a6FAAAEEQEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkRoS4AgLUVlJSf8ZiicpcqXW7v3yuukKvyx23x0RFyOPhuB8A/BCEAITVt7qozHmMkFcXEeG2bkvOtbKc8jo2K0C0jeigzPTWwBQJo1ghCAMKSsdkkYzyPi8oqNXfxdmWc01b2MOsZinE65LDbznwggIAjCPmQnZ2t7OxsuVyuUJcCNCvx0RGKjYpQcVllg89VHB1dbVuRpEcW71ZEmAWhaKddo3snKyMtMdSlAJYTXu8WjYS1xoDgcDjsumVED8VG8R3sVKUVbi3cckQutznzwQACincjAI0qMz1VF/VKUWFp3XuFXG6jOStyVVbpPWC6wuXW1n3HAl1iSJRWuFVS4VI8IRFoVPyPA9DoHA67EuMi/fqdMf3aa+GWIyqtcJ/5YACoI4IQgLCQkZaoPqkJKqn4cexeQXGFpuR863Xc1MwuSoh1NnZ5fisud+np5bmhLgOwPIIQgLDhsNu8Lh25Kt06/V6ruEgHl5cA1BmDpQEAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhHzIzs5Wr169NHDgwFCXAgAAgogg5AOrzwMAYA0EIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIQAAYFkEIR+ys7PVq1cvDRw4MNSlAACAICII+ZCVlaWcnBytXbs21KUAAIAgIggBAADLigh1AQAQSAUl5UE5b3x0hBwOvjsCzQ1BCECzMm3uqqCcNzYqQreM6KHM9NSgnB9AaBCEAKAOissq9eLi7bqoV0rQeoaKy11BOW9zF+N0yGG3hboMhCmCEICwFR8dodioCBWXVTbK8xWXVaqwtFKJcZFBOf/Ty3ODct7mLtpp1+jeycpISwx1KQhDXPAGELYcDrtuGdFDsVF8p7Oy0gq3Fm45IpfbhLoUhCHePQCEtcz0VF3UK0WFpYHvFSooKQ/amKMYp0PRTrtKK9xBOb/VlFa4VVLhUjyhGH7iXwyAsOdw2IN2uSpYHHabRvdO1sItRwhDQAgRhAAgRDLSEtUnNUElFQyS9ldxuYsxVQgIghAAhJDDbuNyDhBCDJYGAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRDyITs7W7169dLAgQNDXQoAAAgigpAPWVlZysnJ0dq1a0NdCgAACCKCEAAAsCyCEAAAsCyCEAAAsCyCEAAAsCyCEAAAsCyCEAAAsCyCEAAAsCyCEAAAsCyCEAAAsCyCEAAAsCyCEAAAsKyIUBcAAEBz4nK5VFFREeoymj2n0ymHw9Hg8xCEAAAIAGOMDh8+rOPHj4e6FMto2bKlUlJSZLPZ6n0OghAAAAFQFYKSkpIUGxvboA9n1M4Yo+LiYuXl5UmS2rdvX+9zEYQAAGggl8vlCUFt2rQJdTmWEBMTI0nKy8tTUlJSvS+TMVgaAIAGqhoTFBsbG+JKrKXq9W7ImCyCEAAAAcLlsMYViNebIAQAACyLIAQAAJqkm2++Wddcc01Qn4MgBAAA6u2BBx5Qv379Ql1GvXHXGAAAAWaMUUFxaCdVTIh1MmapDghCAAAEWEFxhSY+vTykNbw0dZgS4yLrdOxHH32khx9+WFu2bJHD4dDQoUP19NNP65xzzpEkffvtt5oxY4YWLVqksrIy9ezZU9nZ2dq2bZsefPBBST8OXJ43b56GDRumLl26aOPGjZ7eouPHj6tVq1ZatmyZhg0bJpfLpVtvvVWffPKJDh8+rE6dOum3v/2tpk6dGvgXoxYEIQAALK6oqEjTp09Xnz59VFhYqPvuu09jxozRpk2bVFxcrMzMTHXo0EHvvfeeUlJStGHDBrndbo0dO1ZbtmzRRx99pI8//liSlJiYqCNHjpzxOd1ut9LS0vTmm2+qTZs2WrVqlW699Va1b99eP//5z4PdZA+CkA/Z2dnKzs6Wy+UKdSkAAATddddd5/X4pZdeUrt27ZSTk6NVq1bpu+++09q1a9W6dWtJUteuXT3HxsfHKyIiQikpKX49p9Pp9PQmSVKXLl20evVqvfHGG40ahBgs7UNWVpZycnK0du3aUJcCAEDQ7dq1SzfccIPOPvtsJSQkqHPnzpKkffv2adOmTcrIyPCEoEDKzs5W//791a5dO8XHx2vu3Lnat29fwJ+nNvQIAQAQYAmxTr00dVjIa6irK6+8UmeddZZeeOEFpaamyu12q3fv3iovL/csZeEPu/1kP4sxxrPt9NmfX3vtNd1555168sknNXToULVo0UJPPPGEvvjiC7+fryEIQgAABJjNZqvzQOVQ+/7777Vjxw698MILuvjiiyVJn376qWd/nz599OKLL+qHH37w2SsUGRlZbShJu3btJEmHDh1SRkaGJGnTpk1ex3z22We64IIL9Nvf/tazbc+ePQFpkz+4NAYAgIW1atVKbdq00dy5c7V792598sknmj59umf/DTfcoJSUFF1zzTX67LPP9PXXX+uf//ynVq9eLUnq3LmzcnNztWnTJh09elRlZWWKiYnRkCFD9Nhjj2nbtm1asWKF7rnnHq/n7datm9atW6dFixZp586duvfee0MyJIUgBACAhdntdr322mtav369evfurTvuuENPPPGEZ39kZKQWL16spKQkXX755UpPT9djjz3mWe39uuuu02WXXaZLLrlE7dq106uvvirp5IDryspK9e/fX9OmTdPDDz/s9by/+c1vdO2112rs2LEaPHiwvv/+e6/eocZiM6dewIOXgoICJSYmKj8/XwkJCaEuB0Ajyy8qrzYXjD9zsyB4CssqNWvxbq9tM0d0VXxUaEZ8lJaWKjc3V126dFF0dHRIarCiml53fz6/6RECAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAABBN2zYME2bNq3Ox8+fP18tW7YMWj1VCEIAAMCyQrMoCwAAzZgxRkXlrpDWEBfpkM1mC2kN4YAgBABAgBWVu6otCtvY6roI7bBhw5Seni6Hw6G//e1vioyM1MMPP6wbb7xRU6ZM0VtvvaXk5GQ9++yzGjVqlCRpxYoVmjFjhjZv3qzWrVtr/PjxevjhhxURcfL5ioqKNHnyZC1YsEAtWrTQnXfeWe15y8rK9Kc//Umvvvqqjh8/rt69e2v27NkaNmxYQF+HMyEIAYAfCkrKQ10CdDJoVLrcXtsKiivkqnTX8BvBVV5WLrfbqNLlVqXLLZfLLWNMSGqp4vpPLWdijPS3v/1Nd945Q6tWf64333jDE2KuvuYa/eGuP+rpp+fopptu0te53+jYsWO6/PLLNX78eP3973/X9u3bNWnSJEVHR+uBBx6QJM2YMUMrVqzQu+++q6SkJN19993asGGD+vXr53neKVOmKCcnR6+99ppSU1P19ttv67LLLtNXX32lbt26BelVqY4gBAB+mDZ3VahLgCQjqSgmxmvblJxvFaoLQW3i7Prl4NaK+L5IDmeFSipcKi6vDFE1J+07WqgYp+OMx5VWVOrcnr1146TbJUljJ2Zp9uzZio5P1PCrfiFJGn/bHfrf55/XohWfa9mSj5TSvoN+f+8sJSXGqEePHjp48KDuuusu3XfffSouLtZf//pXvfzyy7r00kslnQxaaWlpP9a2b5/mzZunffv2KTU1VZJ055136qOPPtK8efP06KOPBvrlqBFBCADQLBib7WT3RiieOyTPGjjn9jzP82eHw6GWrVqpe48ft7VtlyRJ+uHod9q9a4f69R8oI+m7glLFRkVoyNALVFhYqL379uvYsWMqLy/XgIGD5HKffGUSW7bSueeeK2OMXG6jTZu/lMvlUvfu3b3qKCsrU5s2bYLf4FMQhACgBvHREYqNilBxWWi/2aNuiqOjQ/bcsVE2uW02ue122ex2RUbaNGFwx5DVI0mRTrvcdRosbZMj0im3/ccbyW02e7VtkuQ6uVP6T1vdkg4VlOn7wjJJ0ncnypR/yp8jC0o9v1vhcquo3KXDBaU68N0xORwOfbDsMzkiIpQQ5VBM5MlIEh8f35Bm+40gBAA1cDjsumVED724eDthCH6x2WyKiTzzZalwdE63c7Xo/XdljPHclbb2i9WKb9FC7Tt0UMtWreR0OrVx/Vp16HgyDB4/fkxf79mtIRdeLEnq3aevXC6Xjn73nQZfcKFsNpvaJ0SF5C43ghAA1CIzPVUX9UpRYSlBqClxuY3mrMhVWYgGR5+uRYRbkRFuxTgdiogMr49Wu90mp92u2FPqttmkSIfDa5skRUbYdePNt+hvc/9HD919p8ZN/I0O7t2jJx97RJN++zvZ7XbFxcfrF78cr4fvu1utWrdWm7bt9PjDD8h+Su/S2V27aczPfqFpk2/RvQ/PUu8+/bS3pEDLl32iPn366Iorrmi09ofX3xYAhIDDYVdiXGSoy8BpxvRrr4Vbjqi0IvRhyOGQbHJXXTUKPz7qrqktye1TNfeVt/T4/7tHb1x6gVq1aqVf/HK8pt75R88x9/y/R1VUVKSbb7he8fHxujVrqgoKCrzO81T2/+rp/35MD90zU4cPHVTbtm01ZMgQjR49OhgtrJHNhPr+viasoKBAiYmJys/PV0JCQqjLAQCcxuU2KqkI7cSFklRWVqrD3+5T585dFB3CsUrB5nIb7fvuhNe2Tu1ayGH3L/25jVHeiTKvbSkJ0X6fp7S0VLm5uerSxft19+fzmx4hAEDYcthtdZo0MNgiTITsNpscdpvfH+bhxFffid0m/9sc+k48D9YaAwAAlkUQAgAAlkUQAgAAlkUQAgAgQLj/qHEF4vUmCAEA0EBOp1OSVFxcHOJKrKXq9a56/esj9EPtAQAIcw6HQy1btlReXp4kKTY2NiSzJAdbpcstV0W517bS0lJFOPzrV3G5jSrLvW+fLy2t+91nxhgVFxcrLy9PLVu2lMNR/1m8CUIAAARASkqKJHnCUHPkdht9f6LUa1vliWjZ6zGPUEGJ92zthTEnpyDwR8uWLT2ve30RhHzIzs5Wdna2XK7QT9IFAAgPNptN7du3V1JSkioqKkJdTlCcKC7X0x+v8dr2yE2D1CLWv5nXi8or9d5n+7y23XphJ8X5sTyJ0+lsUE9QFYKQD1lZWcrKyvLMTAkAQF05HI6AfEA3RWUuu74v8p4NMTIqWtHR/gWhSlulCiu9L6dFRUUrOgSTYzJYGgAAWBZBCAAAWBZBCAAAWBZjhGpRNVFTQUFBiCsBACD0CorKVVFa5L2toEA2l39jhArLKlVWXFjtPO4AjRGq+tyuy4SLNsM0mDX69ttv1bFjx1CXAQAA6mH//v1KS0ur9RiCUC3cbrcOHjyoFi1aBHRirIKCAnXs2FH79+9XQkJCwM7bFNC28NWc20fbwlNzbpvUvNsX6rYZY3TixAmlpqbKbq99FBCXxmpht9vPmCQbIiEhodn9469C28JXc24fbQtPzbltUvNuXyjbVtfpbxgsDQAALIsgBAAALIsgFAJRUVG6//77FRUVFepSAo62ha/m3D7aFp6ac9uk5t2+cGobg6UBAIBl0SMEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyDUyLKzs9W5c2dFR0dr8ODBWrNmTahL8tusWbM0cOBAtWjRQklJSbrmmmu0Y8cOr2NKS0uVlZWlNm3aKD4+Xtddd52OHDkSoorr77HHHpPNZtO0adM828K9bQcOHNAvf/lLtWnTRjExMUpPT9e6des8+40xuu+++9S+fXvFxMRo+PDh2rVrVwgrrhuXy6V7771XXbp0UUxMjM455xw99NBDXmsNhVPbVq5cqSuvvFKpqamy2Wx65513vPbXpS0//PCDxo0bp4SEBLVs2VK//vWvVVjovb5TKNTWtoqKCt11111KT09XXFycUlNT9atf/UoHDx70Okc4tu10t912m2w2m+bMmeO1PZzbtm3bNl111VVKTExUXFycBg4cqH379nn2N8X3T4JQI3r99dc1ffp03X///dqwYYP69u2rkSNHKi8vL9Sl+WXFihXKysrS559/riVLlqiiokIjRoxQUdGPC/Hdcccd+te//qU333xTK1as0MGDB3XttdeGsGr/rV27Vv/7v/+rPn36eG0P57YdO3ZMF154oZxOpz788EPl5OToySefVKtWrTzHPP7443rmmWf0/PPP64svvlBcXJxGjhyp0tLSEFZ+ZrNnz9Zzzz2nv/zlL9q2bZtmz56txx9/XM8++6znmHBqW1FRkfr27avs7Gyf++vSlnHjxmnr1q1asmSJFi5cqJUrV+rWW29trCbUqLa2FRcXa8OGDbr33nu1YcMGLViwQDt27NBVV13ldVw4tu1Ub7/9tj7//HOlpqZW2xeubduzZ48uuugi9ejRQ8uXL9eXX36pe++9V9HR0Z5jmuT7p0GjGTRokMnKyvI8drlcJjU11cyaNSuEVTVcXl6ekWRWrFhhjDHm+PHjxul0mjfffNNzzLZt24wks3r16lCV6ZcTJ06Ybt26mSVLlpjMzEwzdepUY0z4t+2uu+4yF110UY373W63SUlJMU888YRn2/Hjx01UVJR59dVXG6PEerviiivMxIkTvbZde+21Zty4ccaY8G6bJPP22297HtelLTk5OUaSWbt2reeYDz/80NhsNnPgwIFGq/1MTm+bL2vWrDGSzN69e40x4d+2b7/91nTo0MFs2bLFnHXWWebPf/6zZ184t23s2LHml7/8ZY2/01TfP+kRaiTl5eVav369hg8f7tlmt9s1fPhwrV69OoSVNVx+fr4kqXXr1pKk9evXq6KiwqutPXr0UKdOncKmrVlZWbriiiu82iCFf9vee+89DRgwQD/72c+UlJSkjIwMvfDCC579ubm5Onz4sFf7EhMTNXjw4CbfvgsuuEBLly7Vzp07JUmbN2/Wp59+qlGjRkkK77adri5tWb16tVq2bKkBAwZ4jhk+fLjsdru++OKLRq+5IfLz82Wz2dSyZUtJ4d02t9utm266STNmzNB5551XbX+4ts3tduv9999X9+7dNXLkSCUlJWnw4MFel8+a6vsnQaiRHD16VC6XS8nJyV7bk5OTdfjw4RBV1XBut1vTpk3ThRdeqN69e0uSDh8+rMjISM+bVpVwaetrr72mDRs2aNasWdX2hXvbvv76az333HPq1q2bFi1apMmTJ+v222/X3/72N0nytCEc/53+8Y9/1C9+8Qv16NFDTqdTGRkZmjZtmsaNGycpvNt2urq05fDhw0pKSvLaHxERodatW4dVe0tLS3XXXXfphhtu8CzeGc5tmz17tiIiInT77bf73B+ubcvLy1NhYaEee+wxXXbZZVq8eLHGjBmja6+9VitWrJDUdN8/WX0eDZKVlaUtW7bo008/DXUpAbF//35NnTpVS5Ys8bqu3Vy43W4NGDBAjz76qCQpIyNDW7Zs0fPPP6/x48eHuLqGeeONN/TKK6/oH//4h8477zxt2rRJ06ZNU2pqati3zaoqKir085//XMYYPffcc6Eup8HWr1+vp59+Whs2bJDNZgt1OQHldrslSVdffbXuuOMOSVK/fv20atUqPf/888rMzAxlebWiR6iRtG3bVg6Ho9ro+CNHjiglJSVEVTXMlClTtHDhQi1btkxpaWme7SkpKSovL9fx48e9jg+Htq5fv155eXk6//zzFRERoYiICK1YsULPPPOMIiIilJycHLZtk6T27durV69eXtt69uzpuaujqg3h+O90xowZnl6h9PR03XTTTbrjjjs8PXvh3LbT1aUtKSkp1W7EqKys1A8//BAW7a0KQXv37tWSJUs8vUFS+Lbt3//+t/Ly8tSpUyfP+8vevXv1+9//Xp07d5YUvm1r27atIiIizvj+0hTfPwlCjSQyMlL9+/fX0qVLPdvcbreWLl2qoUOHhrAy/xljNGXKFL399tv65JNP1KVLF6/9/fv3l9Pp9Grrjh07tG/fvibf1ksvvVRfffWVNm3a5PkZMGCAxo0b5/lzuLZNki688MJqUx3s3LlTZ511liSpS5cuSklJ8WpfQUGBvvjiiybfvuLiYtnt3m9pDofD8001nNt2urq0ZejQoTp+/LjWr1/vOeaTTz6R2+3W4MGDG71mf1SFoF27dunjjz9WmzZtvPaHa9tuuukmffnll17vL6mpqZoxY4YWLVokKXzbFhkZqYEDB9b6/tJkPxtCNkzbgl577TUTFRVl5s+fb3Jycsytt95qWrZsaQ4fPhzq0vwyefJkk5iYaJYvX24OHTrk+SkuLvYcc9ttt5lOnTqZTz75xKxbt84MHTrUDB06NIRV19+pd40ZE95tW7NmjYmIiDCPPPKI2bVrl3nllVdMbGysefnllz3HPPbYY6Zly5bm3XffNV9++aW5+uqrTZcuXUxJSUkIKz+z8ePHmw4dOpiFCxea3Nxcs2DBAtO2bVvzhz/8wXNMOLXtxIkTZuPGjWbjxo1GknnqqafMxo0bPXdO1aUtl112mcnIyDBffPGF+fTTT023bt3MDTfcEKomedTWtvLycnPVVVeZtLQ0s2nTJq/3mLKyMs85wrFtvpx+15gx4du2BQsWGKfTaebOnWt27dplnn32WeNwOMy///1vzzma4vsnQaiRPfvss6ZTp04mMjLSDBo0yHz++eehLslvknz+zJs3z3NMSUmJ+e1vf2tatWplYmNjzZgxY8yhQ4dCV3QDnB6Ewr1t//rXv0zv3r1NVFSU6dGjh5k7d67Xfrfbbe69916TnJxsoqKizKWXXmp27NgRomrrrqCgwEydOtV06tTJREdHm7PPPtv86U9/8vrwDKe2LVu2zOf/s/Hjxxtj6taW77//3txwww0mPj7eJCQkmAkTJpgTJ06EoDXeamtbbm5uje8xy5Yt85wjHNvmi68gFM5t++tf/2q6du1qoqOjTd++fc0777zjdY6m+P5pM+aUaVcBAAAshDFCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCQIjcfPPNuuaaaxr9eefPn6+WLVs2+vM2JTabTe+8806N+7/55hvZbDZt2rQpKOevj++//15JSUn65ptvGnSeYcOGadq0aQGpKZhycnKUlpamoqKiUJeCZo4gBASBzWar9eeBBx7Q008/rfnz54e61HoLxod9U9GxY0cdOnRIvXv3rvW4Bx54QP369WuUmh555BFdffXVnlXK62vBggV66KGHAlPUfwQjXPfq1UtDhgzRU089FdDzAqeLCHUBQHN06NAhz59ff/113XfffV6rMsfHxys+Pj4UpaEOHA6HUlJSatxvjJHL5Wq0eoqLi/XXv/7Vs0J5Q7Ru3ToAFTWOCRMmaNKkSZo5c6YiIvi4QnDQIwQEQUpKiucnMTFRNpvNa1t8fHy1S2PDhg3T7373O02bNk2tWrVScnKyXnjhBRUVFWnChAlq0aKFunbtqg8//NDrubZs2aJRo0YpPj5eycnJuummm3T06NEz1vjOO++oW7duio6O1siRI7V//36v/e+++67OP/98RUdH6+yzz9aDDz6oyspKSfL0SowZM0Y2m02dO3dWfn6+HA6H1q1bJ0lyu91q3bq1hgwZ4jnnyy+/rI4dO3oe79+/Xz//+c/VsmVLtW7dWldffXW1Sz8vvviievbsqejoaPXo0UP/8z//49lXdQlrwYIFuuSSSxQbG6u+fftq9erVZ2z/oUOHNGrUKMXExOjss8/WW2+9Ve28VZfGli9fLpvNpg8//FD9+/dXVFSUXn75ZT344IPavHmzp6fv1B6+o0ePasyYMYqNjVW3bt303nvvefYdO3ZM48aNU7t27RQTE6Nu3bpp3rx5Ndb6wQcfKCoqyuu1rKpp0aJFysjIUExMjP7rv/5LeXl5+vDDD9WzZ08lJCToxhtvVHFxsef3Tr801rlzZz366KOaOHGiWrRooU6dOmnu3LnVnuf48eOebZs2bZLNZtM333yj5cuXa8KECcrPz/fq8ZSksrIy3XnnnerQoYPi4uI0ePBgLV++3HOevXv36sorr1SrVq0UFxen8847Tx988IFn/09/+lP98MMPWrFiRY2vDdBgIV3yFbCAefPmmcTExGrbx48fb66++mrP48zMTNOiRQvz0EMPmZ07d5qHHnrIOBwOM2rUKDN37lyzc+dOM3nyZNOmTRtTVFRkjDHm2LFjpl27dmbmzJlm27ZtZsOGDeanP/2pueSSS2qtx+l0mgEDBphVq1aZdevWmUGDBpkLLrjAc8zKlStNQkKCmT9/vtmzZ49ZvHix6dy5s3nggQeMMcbk5eUZSWbevHnm0KFDJi8vzxhjzPnnn2+eeOIJY4wxmzZtMq1btzaRkZGelbNvueUWM27cOGOMMeXl5aZnz55m4sSJ5ssvvzQ5OTnmxhtvNOeee65nxfiXX37ZtG/f3vzzn/80X3/9tfnnP/9pWrdubebPn2+MMZ6Vynv06GEWLlxoduzYYa6//npz1llnmYqKihpfA0mmTZs25oUXXjA7duww99xzj3E4HCYnJ8frvBs3bjTG/Ljqdp8+fczixYvN7t27zbfffmt+//vfm/POO88cOnTIHDp0yBQXF3vOn5aWZv7xj3+YXbt2mdtvv93Ex8eb77//3hhjTFZWlunXr59Zu3atyc3NNUuWLDHvvfdejfXefvvt5rLLLvPaVlXTkCFDzKeffmo2bNhgunbtajIzM82IESPMhg0bzMqVK02bNm3MY4895vm9zMxMM3XqVM/js846y7Ru3dpkZ2ebXbt2mVmzZhm73W62b9/u9TzHjh3z/M7GjRuNJJObm2vKysrMnDlzTEJCgud1OPXv+4ILLjArV640u3fvNk888YSJiooyO3fuNMYYc8UVV5if/vSn5ssvvzR79uwx//rXv8yKFSu82jl48GBz//331/jaAA1FEAKCzJ8gdNFFF3keV1ZWmri4OHPTTTd5th06dMhIMqtXrzbGGPPQQw+ZESNGeJ13//79RpLZsWNHjfVIMp9//rln27Zt24wk88UXXxhjjLn00kvNo48+6vV7//d//2fat2/veSzJvP32217HTJ8+3VxxxRXGGGPmzJljxo4da/r27Ws+/PBDY4wxXbt2NXPnzvWc79xzzzVut9vz+2VlZSYmJsYsWrTIGGPMOeecY/7xj394PcdDDz1khg4daoz5MbC8+OKLnv1bt241ksy2bdt8tr+q9ttuu81r2+DBg83kyZO9znt6EHrnnXe8fuf+++83ffv29Xn+e+65x/O4sLDQSPK8DldeeaWZMGFCjfWd7uqrrzYTJ0702lZV08cff+zZNmvWLCPJ7Nmzx7PtN7/5jRk5cqTnsa8g9Mtf/tLz2O12m6SkJPPcc895PU9NQcgY3//G9+7daxwOhzlw4IDX9ksvvdTMnDnTGGNMenq6J1zXZMyYMebmm2+u9RigIbjoCjQhffr08fzZ4XCoTZs2Sk9P92xLTk6WJOXl5UmSNm/erGXLlvkcb7Rnzx51797d5/NERERo4MCBnsc9evRQy5YttW3bNg0aNEibN2/WZ599pkceecRzjMvlUmlpqYqLixUbG+vzvJmZmfrrX/8ql8ulFStWaMSIEUpJSdHy5cvVp08f7d69W8OGDfPUvnv3brVo0cLrHKWlpdqzZ4+Kioq0Z88e/frXv9akSZM8+ysrK5WYmFjj69a+fXvPa9SjRw+fdUrS0KFDqz0+011iAwYMqHV/TTXFxcUpISHB8/c2efJkXXfdddqwYYNGjBiha665RhdccEGN5yopKVF0dPQZnyc5OVmxsbE6++yzvbatWbOmzrVWXcatqrW+vvrqK7lcrmr/BsvKytSmTRtJ0u23367Jkydr8eLFGj58uK677jqvWiQpJibG69IeEGgEIaAJcTqdXo9tNpvXNpvNJunk+BtJKiws1JVXXqnZs2dXO1dVIKiPwsJCPfjgg7r22mur7avpA1mSfvKTn+jEiRPasGGDVq5cqUcffVQpKSl67LHH1LdvX6Wmpqpbt26e5+jfv79eeeWVaudp166dCgsLJUkvvPCCBg8e7LXf4XB4Pa7tNQqkuLi4Oh/r6++yqqZRo0Zp7969+uCDD7RkyRJdeumlysrK0n//93/7PFfbtm117NixMz7P6f9eTn/e+tRqt58cSmqM8eyvqKio9XzSyb9fh8Oh9evXV/v7qgrut9xyi0aOHKn3339fixcv1qxZs/Tkk0/qd7/7nefYH374Qeecc84Znw+oL4IQEMbOP/98/fOf/1Tnzp39uqumsrJS69at06BBgyRJO3bs0PHjx9WzZ0/PeXfs2KGuXbvWeA6n01ntzqmWLVuqT58++stf/iKn06kePXooKSlJY8eO1cKFC5WZmelV++uvv66kpCQlJCRUO39iYqJSU1P19ddfa9y4cXVuW119/vnn+tWvfuX1OCMjw69zREZG1vvusXbt2mn8+PEaP368Lr74Ys2YMaPGIJSRkaGXX365Xs/TUO3atZN0cnB5q1atJKlaz5mv1yEjI0Mul0t5eXm6+OKLazx/x44dddttt+m2227TzJkz9cILL3gFoS1btuj6668PUGuA6rhrDAhjWVlZ+uGHH3TDDTdo7dq12rNnjxYtWqQJEybU+gHtdDr1u9/9Tl988YXWr1+vm2++WUOGDPEEo/vuu09///vf9eCDD2rr1q3atm2bXnvtNd1zzz2ec3Tu3FlLly7V4cOHvXorhg0bpldeecUTelq3bq2ePXvq9ddf9wpC48aNU9u2bXX11Vfr3//+t3Jzc7V8+XLdfvvt+vbbbyVJDz74oGbNmqVnnnlGO3fu1FdffaV58+YFZG6ZN998Uy+99JJ27typ+++/X2vWrNGUKVP8Okfnzp2Vm5urTZs26ejRoyorK6vT791333169913tXv3bm3dulULFy70hFBfRo4cqa1bt9bYKxRMXbt2VceOHfXAAw9o165dev/99/Xkk096HdO5c2cVFhZq6dKlOnr0qIqLi9W9e3eNGzdOv/rVr7RgwQLl5uZqzZo1mjVrlt5//31J0rRp07Ro0SLl5uZqw4YNWrZsmdfr8M033+jAgQMaPnx4o7YZ1kIQAsJYamqqPvvsM7lcLo0YMULp6emaNm2aWrZs6bmk4UtsbKzuuusu3XjjjbrwwgsVHx+v119/3bN/5MiRWrhwoRYvXqyBAwdqyJAh+vOf/6yzzjrLc8yTTz6pJUuWqGPHjl49KZmZmXK5XJ6xQNLJcHT6ttjYWK1cuVKdOnXStddeq549e+rXv/61SktLPT1Et9xyi1588UXNmzdP6enpyszM1Pz589WlS5cGv3YPPvigXnvtNfXp00d///vf9eqrr6pXr15+neO6667TZZddpksuuUTt2rXTq6++Wqffi4yM1MyZM9WnTx/95Cc/kcPh0GuvvVbj8enp6Tr//PP1xhtv+FVfIDidTr366qvavn27+vTpo9mzZ+vhhx/2OuaCCy7QbbfdprFjx6pdu3Z6/PHHJUnz5s3Tr371K/3+97/Xueeeq2uuuUZr165Vp06dJJ0cd5aVlaWePXvqsssuU/fu3b2mR3j11Vc1YsQIr393QKDZzKkXfgEATdL777+vGTNmaMuWLbWG3OaivLxc3bp10z/+8Q9deOGFoS4HzRhjhAAgDFxxxRXatWuXDhw44DUpZXO1b98+3X333YQgBB09QgAAwLKaf/8qAABADQhCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAsv4/a8xSo9PxtnEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "model = thinkstats2.Cdf(sample, label='model')\n",
    "    \n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Cdfs([cdf, model], complement=True)\n",
    "thinkplot.Config(xlabel='Time between births (minutes)',\n",
    "                ylabel='CCDF',\n",
    "                yscale='log')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "48885ea5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# If you plot distributions for a large number of samples, you get a sense\n",
    "# of how much random variation to expect.  In this case, the data fall within\n",
    "# the range we expect, so there is no compelling reason to think it is\n",
    "# not exponential.\n",
    "\n",
    "for i in range(100):\n",
    "    sample = [random.expovariate(lam) for _ in range(n)]\n",
    "    thinkplot.Cdf(thinkstats2.Cdf(sample), complement=True, color=\"0.9\")\n",
    "\n",
    "thinkplot.Cdf(cdf, complement=True)\n",
    "thinkplot.Config(xlabel=\"Time between births (minutes)\", ylabel=\"CCDF\", yscale=\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e6d2633",
   "metadata": {},
   "source": [
    "**Bonus Example:** The distributions of wealth and income are sometimes modeled using lognormal and Pareto distributions. To see which is better, let’s look at some data.\n",
    "\n",
    "The Current Population Survey (CPS) is a joint effort of the Bureau of Labor Statistics and the Census Bureau to study income and related variables. Data collected in 2013 is available from http://www.census.gov/hhes/www/cpstables/032013/hhinc/toc.htm. I downloaded `hinc06.xls`, which is an Excel spreadsheet with information about household income, and converted it to `hinc06.csv`, a CSV file you will find in the repository for this book. You will also find `hinc.py`, which reads this file.\n",
    "\n",
    "Extract the distribution of incomes from this dataset. Are any of the analytic distributions in this chapter a good model of the data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "ad2e597a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloaded hinc.py\n",
      "Downloaded hinc06.csv\n"
     ]
    }
   ],
   "source": [
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/hinc.py\")\n",
    "download(\"https://github.com/AllenDowney/ThinkStats2/raw/master/code/hinc06.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "6461d780",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>income</th>\n",
       "      <th>freq</th>\n",
       "      <th>cumsum</th>\n",
       "      <th>ps</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4999.0</td>\n",
       "      <td>4204</td>\n",
       "      <td>4204</td>\n",
       "      <td>0.034330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9999.0</td>\n",
       "      <td>4729</td>\n",
       "      <td>8933</td>\n",
       "      <td>0.072947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14999.0</td>\n",
       "      <td>6982</td>\n",
       "      <td>15915</td>\n",
       "      <td>0.129963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19999.0</td>\n",
       "      <td>7157</td>\n",
       "      <td>23072</td>\n",
       "      <td>0.188407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24999.0</td>\n",
       "      <td>7131</td>\n",
       "      <td>30203</td>\n",
       "      <td>0.246640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>29999.0</td>\n",
       "      <td>6740</td>\n",
       "      <td>36943</td>\n",
       "      <td>0.301679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>34999.0</td>\n",
       "      <td>6354</td>\n",
       "      <td>43297</td>\n",
       "      <td>0.353566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>39999.0</td>\n",
       "      <td>5832</td>\n",
       "      <td>49129</td>\n",
       "      <td>0.401191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>44999.0</td>\n",
       "      <td>5547</td>\n",
       "      <td>54676</td>\n",
       "      <td>0.446488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>49999.0</td>\n",
       "      <td>5254</td>\n",
       "      <td>59930</td>\n",
       "      <td>0.489392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>54999.0</td>\n",
       "      <td>5102</td>\n",
       "      <td>65032</td>\n",
       "      <td>0.531056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>59999.0</td>\n",
       "      <td>4256</td>\n",
       "      <td>69288</td>\n",
       "      <td>0.565810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>64999.0</td>\n",
       "      <td>4356</td>\n",
       "      <td>73644</td>\n",
       "      <td>0.601382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>69999.0</td>\n",
       "      <td>3949</td>\n",
       "      <td>77593</td>\n",
       "      <td>0.633629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>74999.0</td>\n",
       "      <td>3756</td>\n",
       "      <td>81349</td>\n",
       "      <td>0.664301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>79999.0</td>\n",
       "      <td>3414</td>\n",
       "      <td>84763</td>\n",
       "      <td>0.692180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>84999.0</td>\n",
       "      <td>3326</td>\n",
       "      <td>88089</td>\n",
       "      <td>0.719341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>89999.0</td>\n",
       "      <td>2643</td>\n",
       "      <td>90732</td>\n",
       "      <td>0.740923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>94999.0</td>\n",
       "      <td>2678</td>\n",
       "      <td>93410</td>\n",
       "      <td>0.762792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>99999.0</td>\n",
       "      <td>2223</td>\n",
       "      <td>95633</td>\n",
       "      <td>0.780945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>104999.0</td>\n",
       "      <td>2606</td>\n",
       "      <td>98239</td>\n",
       "      <td>0.802226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>109999.0</td>\n",
       "      <td>1838</td>\n",
       "      <td>100077</td>\n",
       "      <td>0.817235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>114999.0</td>\n",
       "      <td>1986</td>\n",
       "      <td>102063</td>\n",
       "      <td>0.833453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>119999.0</td>\n",
       "      <td>1464</td>\n",
       "      <td>103527</td>\n",
       "      <td>0.845408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>124999.0</td>\n",
       "      <td>1596</td>\n",
       "      <td>105123</td>\n",
       "      <td>0.858441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>129999.0</td>\n",
       "      <td>1327</td>\n",
       "      <td>106450</td>\n",
       "      <td>0.869278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>134999.0</td>\n",
       "      <td>1253</td>\n",
       "      <td>107703</td>\n",
       "      <td>0.879510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>139999.0</td>\n",
       "      <td>1140</td>\n",
       "      <td>108843</td>\n",
       "      <td>0.888819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>144999.0</td>\n",
       "      <td>1119</td>\n",
       "      <td>109962</td>\n",
       "      <td>0.897957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>149999.0</td>\n",
       "      <td>920</td>\n",
       "      <td>110882</td>\n",
       "      <td>0.905470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>154999.0</td>\n",
       "      <td>1143</td>\n",
       "      <td>112025</td>\n",
       "      <td>0.914803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>159999.0</td>\n",
       "      <td>805</td>\n",
       "      <td>112830</td>\n",
       "      <td>0.921377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>164999.0</td>\n",
       "      <td>731</td>\n",
       "      <td>113561</td>\n",
       "      <td>0.927347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>169999.0</td>\n",
       "      <td>575</td>\n",
       "      <td>114136</td>\n",
       "      <td>0.932042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>174999.0</td>\n",
       "      <td>616</td>\n",
       "      <td>114752</td>\n",
       "      <td>0.937072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>179999.0</td>\n",
       "      <td>570</td>\n",
       "      <td>115322</td>\n",
       "      <td>0.941727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>184999.0</td>\n",
       "      <td>502</td>\n",
       "      <td>115824</td>\n",
       "      <td>0.945826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>189999.0</td>\n",
       "      <td>364</td>\n",
       "      <td>116188</td>\n",
       "      <td>0.948799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>194999.0</td>\n",
       "      <td>432</td>\n",
       "      <td>116620</td>\n",
       "      <td>0.952327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>199999.0</td>\n",
       "      <td>378</td>\n",
       "      <td>116998</td>\n",
       "      <td>0.955413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>249999.0</td>\n",
       "      <td>2549</td>\n",
       "      <td>119547</td>\n",
       "      <td>0.976229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>inf</td>\n",
       "      <td>2911</td>\n",
       "      <td>122458</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      income  freq  cumsum        ps\n",
       "0     4999.0  4204    4204  0.034330\n",
       "1     9999.0  4729    8933  0.072947\n",
       "2    14999.0  6982   15915  0.129963\n",
       "3    19999.0  7157   23072  0.188407\n",
       "4    24999.0  7131   30203  0.246640\n",
       "5    29999.0  6740   36943  0.301679\n",
       "6    34999.0  6354   43297  0.353566\n",
       "7    39999.0  5832   49129  0.401191\n",
       "8    44999.0  5547   54676  0.446488\n",
       "9    49999.0  5254   59930  0.489392\n",
       "10   54999.0  5102   65032  0.531056\n",
       "11   59999.0  4256   69288  0.565810\n",
       "12   64999.0  4356   73644  0.601382\n",
       "13   69999.0  3949   77593  0.633629\n",
       "14   74999.0  3756   81349  0.664301\n",
       "15   79999.0  3414   84763  0.692180\n",
       "16   84999.0  3326   88089  0.719341\n",
       "17   89999.0  2643   90732  0.740923\n",
       "18   94999.0  2678   93410  0.762792\n",
       "19   99999.0  2223   95633  0.780945\n",
       "20  104999.0  2606   98239  0.802226\n",
       "21  109999.0  1838  100077  0.817235\n",
       "22  114999.0  1986  102063  0.833453\n",
       "23  119999.0  1464  103527  0.845408\n",
       "24  124999.0  1596  105123  0.858441\n",
       "25  129999.0  1327  106450  0.869278\n",
       "26  134999.0  1253  107703  0.879510\n",
       "27  139999.0  1140  108843  0.888819\n",
       "28  144999.0  1119  109962  0.897957\n",
       "29  149999.0   920  110882  0.905470\n",
       "30  154999.0  1143  112025  0.914803\n",
       "31  159999.0   805  112830  0.921377\n",
       "32  164999.0   731  113561  0.927347\n",
       "33  169999.0   575  114136  0.932042\n",
       "34  174999.0   616  114752  0.937072\n",
       "35  179999.0   570  115322  0.941727\n",
       "36  184999.0   502  115824  0.945826\n",
       "37  189999.0   364  116188  0.948799\n",
       "38  194999.0   432  116620  0.952327\n",
       "39  199999.0   378  116998  0.955413\n",
       "40  249999.0  2549  119547  0.976229\n",
       "41       inf  2911  122458  1.000000"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import hinc\n",
    "\n",
    "df = hinc.ReadData()\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cb2fd41",
   "metadata": {},
   "source": [
    "Here's what the CDF looks like on a linear scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "76bfde61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs, ps = df.income.values, df.ps.values\n",
    "cdf = thinkstats2.Cdf(xs, ps, label=\"data\")\n",
    "cdf_log = thinkstats2.Cdf(np.log10(xs), ps, label=\"data\")\n",
    "\n",
    "# linear plot\n",
    "thinkplot.Cdf(cdf)\n",
    "thinkplot.Config(xlabel=\"household income\", ylabel=\"CDF\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f29e5454",
   "metadata": {},
   "source": [
    "To check whether a Pareto model describes the data well, I plot the CCDF on a log-log scale.\n",
    "\n",
    "I found parameters for the Pareto model that match the tail of the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "aa01a710",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs, ys = thinkstats2.RenderParetoCdf(xmin=55000, alpha=2.5, low=0, high=250000)\n",
    "\n",
    "thinkplot.Plot(xs, 1 - ys, label=\"model\", color=\"0.8\")\n",
    "\n",
    "thinkplot.Cdf(cdf, complement=True)\n",
    "thinkplot.Config(\n",
    "    xlabel=\"log10 household income\",\n",
    "    ylabel=\"CCDF\",\n",
    "    xscale=\"log\",\n",
    "    yscale=\"log\",\n",
    "    loc=\"lower left\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "557a7734",
   "metadata": {},
   "source": [
    "For the lognormal model I estimate mu and sigma using percentile-based statistics (median and IQR)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "b5ca3485",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.740354793159152 0.35\n"
     ]
    }
   ],
   "source": [
    "median = cdf_log.Percentile(50)\n",
    "iqr = cdf_log.Percentile(75) - cdf_log.Percentile(25)\n",
    "std = iqr / 1.349\n",
    "\n",
    "# choose std to match the upper tail\n",
    "std = 0.35\n",
    "print(median, std)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcaaaba7",
   "metadata": {},
   "source": [
    "Here's what the distribution, and fitted model, look like on a log-x scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "f54aafa8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs, ps = thinkstats2.RenderNormalCdf(median, std, low=3.5, high=5.5)\n",
    "thinkplot.Plot(xs, ps, label=\"model\", color=\"0.8\")\n",
    "\n",
    "thinkplot.Cdf(cdf_log)\n",
    "thinkplot.Config(xlabel=\"log10 household income\", ylabel=\"CDF\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85a83604",
   "metadata": {},
   "source": [
    "My conclusions based on these figures are:\n",
    "\n",
    "1) The Pareto model might be a reasonable choice for the top\n",
    "   10-20% of incomes.\n",
    "\n",
    "2) The lognormal model captures the shape of the distribution better,\n",
    "   with some deviation in the left tail.  With different\n",
    "   choices for sigma, you could match the upper or lower tail, but not\n",
    "   both at the same time.\n",
    " \n",
    "In summary I would say that neither model captures the whole distribution,\n",
    "so you might have to \n",
    "\n",
    "1) look for another analytic model, \n",
    "\n",
    "2) choose one that captures the part of the distribution that is most \n",
    "   relevent, or \n",
    "\n",
    "3) avoid using an analytic model altogether."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0bb5d2ca",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
